When I assembled my lathe, the bed was too short for my use, so I bought the 16" upgrade kit from LMS.
As part of installing that kit, I relocated the rack several times.
Each time, I made sure I minimized the play between the rack and drive gear.
The first time, I put it where the instructions said and the rack moved between drilling holes.
The second time, I moved it closer to the head to drill new holes, but the rack wasn't close enough to the head end and I could advance the apron off the head end of the rack.
The third time, I got everything right and haven't moved it since.
As I said in the previous post, when I installed the bearings in the apron for the carriage wheel shaft, I bored the hole offset .004 closer to the shaft that has the gear that contacts the rack. This reduced the play between the gears by more than half.
By adding the bearings and relocating the rack gear, I was able to reduce the total play from more than 180 degrees to less than 30 degrees of rotation of the carriage feed wheel.
By the way Bazmak, as you said, there isn't enough metal to slot the holes, but there is enough space to adjust the rack position before tightening the mounting screws.
As an aside, the kit from LMS was on sale for $99.99 when I bought it. Shortly after, it went to $129.95. The kit includes the bed, new swarf tray, extended rack gear and feed screw. They sell the bed by itself for $161.95. Go figure.
The longer bed made a huge difference in the useability of the lathe. The only downside is that the increase in weight has made it too heavy to move around, which is originally why I purchased the lathe.